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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02434 |
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Table of Contents:
- We prove a sharp stability estimate for Schur iterates of contractive analytic functions in the open unit disk. We then apply this result in the setting of the inverse scattering approach and obtain a fast algorithm for solving the discrete integrable nonlinear Schrödinger equation (Ablowitz-Ladik equation) on the integer lattice, $\mathbb{Z}$. We also give a self-contained introduction to the theory of the nonlinear Fourier transform from the perspective of Schur functions and orthogonal polynomials on the unit circle.